Development and Application of SST-SAS Turbulence...

© 2007 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

Development and Application of SST-SAS

Turbulence Model in the DESIDER Project

Y. Egorov, F. MenterANSYS Germany

[email protected]


Outline

• Scale-Adaptive Simulation (SAS) concept

• SST-SAS turbulence model

• Aerodynamic applications

– NACA0021 airfoil beyond stall

– Delta wing

– Full aircraft configuration

– 3-D acoustic cavity


SAS concept

• URANS: unphysical single mode

unsteady behaviour

• LES: too expensive

• DES:

– 1st industrial model of high Re

flows with LES content

– Explicit mix of RANS & LES →→→→grid sensitivity

• SAS: provides URANS with LES

content in unsteady regions

URANS

SAS-URANS


SAS concept. Turbulence scales

• Two scales required for statistical description

• Two equations

→→→→ two scales?

E(k) spectrumL, T


• k-ω model

• One local scale: S

• 2nd scale:

– Shear layer thickness via diffusion: L = κκκκ·y , L = δδδδ

– Too dissipative to resolve the energy cascade

– Homogeneous turbulence,

frozen LES velocity field:

No diffusion →→→→ Contradiction:

SAS concept. 2-eq RANS models

( ) ( )kDiffcSDt

Dkt +ω−ν= µ

22

( )ω+ωβ−α=ω

DiffSDt

D 22

22 ω= µcS22 ωβ=α S


SAS concept. v.Karman length scale

• Rotta’s transport eq. for spatial correlation-based L

• 2nd scale from ∂2U/∂y2 →→→→ von Karman length scale

• New RANS model for k and

• Two natural local scales: S and LvK

Lk=Φ

( )Φ+ζ−

ζ−ζ×

Φ=

ΦDiffk

L

LP

kDt

D

vK

k 3

2

21

U22

, ∇κ=ν= SLSP vKtk


SAS concept. SAS and RANS

• , λ - natural scale, ignored byRANS

• Two

domains:

δ = 4λδ = 8λ

• RANS:

L ~ δ

• SAS:

L ~ λ

⋅=

λ

π yUyU

2sin)( 0

SAS

RANS


SAS concept. SAS and DES

• DES enforces LES-behaviour via explicit grid influence

• SAS detects resolved structures and adjusts accordingly

DES: RANS LES based on ∆∆∆∆

SAS: RANS “LES” based on LvK


SAS concept definition

• SAS: 2nd flow scale in the source terms

typically via 2nd velocity derivative

• Requirements:

– Proper RANS performance in stable

flow region

– Break-up of large unsteady structures

into a turbulent spectrum

– Proper energy dissipation at small

scale (high wave number damping)

No grid & time step dependence

Based on the grid

spacing ∆∆∆∆


SST-SAS turbulence model

• Experimental k-Φ model

• Transformation to k-ω → SST-SAS model

( ) ( )kDiffcSDt

Dkt +ω−ν= µ

22

( ) ( )ω∇∇

ωσ

−⋅+ω++ωβ−α=

ω

ω

kF

DiffQSDt

DSAS

2

22 12

Standard SST

∇

ω

ω∇

σ⋅−

κζ=

Φ

0,,max2

max2

2

2

22

2

2k

kkC

L

LSQ

vK

SAS


SST-SAS turbulence model

• Decay of isotropic turbulence

High wave number damping in SAS:

- off

- on

- LES


NACA0021 airfoil beyond stall

• NACA0021 at 60°AoA, experiment by Swalwell at al., 2003

• Re = 2.7·105, low Mach number, domain span-size 4 chords

• O-grid: courtesy of NTS, Russia, 1.9 million elements, y + ≈ 1

Contours of L / ∆∆∆∆ ∈∈∈∈ [0, 0.5]

Isosurface of

Q = ΩΩΩΩ2 - S2


NACA0021 airfoil beyond stall

• Mean values and

PSD spectra of forces

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

x/c

-Cp

SST-SAS

Experiment

Mean pressure

1.5170.931Experiment

1.4840.915SST-SAS

CDCL


Delta wing

• Sweep angle 76°,

experiment by

Laschka et al., 1995

• AoA = 35°,

Re = 1.07·106,

low Mach number


Delta wing

• Hybrid unstructured grid, 50 million elements, y +≈ 0.5

– Courtesy of EADS Deutschland GmbH, Military Air Systems


Delta wing

L / ∆∆∆∆ Mean Cp

Exp. SST-SAS

• Delayed bursting of vortices predicted: numerical diffusion?


Full aircraft configuration

• Delta-canard FA-5, exp. by Laschka et al., 1995

• AoA = 15°, Re = 2.78·106, low Mach number

• Hybrid unstructured grid, 36 million elements, y +≈ 0.8

– Courtesy of EADSDeutschland GmbH,Military Air Systems

– Half of the airplane,symmetry BC



• SAS vs. URANS



• Resolution details

L / ∆∆∆∆



• Cross planes at x/c = 0.2, 0.4, 0.6, 0.8, 1

U/U0

Experiment SST-SASResolved+Modelled TKE/U0

2

Experiment SST-SAS


3-D acoustic cavity

• M219 test cavity, exp. by QinetiQ, Henshaw, 2000

• Shallow cavity: Length×Width×Depth = 5×1×1, 1=4"

• ReD = 1.37·106, M∞∞∞∞=0.85 – local transonic zones

• Coarse grid,

1.1 million elements

• 90 ∆t per convective unit

• 100 units run

for statistics


3-D acoustic cavity

• Resolved turbulent structures

• Pressure spectrum at cavity bottom near the

downstream wall (K29)

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

0 200 400 600 800 1000

f, Hz

PSD of p

Experiment

SST SAS


Other DESIDER tests simulated

• Bump in a duct,

experiment by ONERA• Generic car mirror,

exp. by Höld et al., 1999

Date post:	04-Apr-2018
Category:	Documents
Upload:	leminh
View:	221 times
Download:	3 times

Development and Application of SST-SAS Turbulence...

Documents